Recent developments in consumer credit risk assessment

Consumer credit risk assessment involves the use of risk assessment tools to manage a borrower’s account from the time of pre-screening a potential application through to the management of the account during its life and possible write-off. The riskiness of lending to a credit applicant is usually estimated using a logistic regression model though researchers have considered many other types of classifier and whilst preliminary evidence suggest support vector machines seem to be the most accurate, data quality issues may prevent these laboratory based results from being achieved in practice. The training of a classifier on a sample of accepted applicants rather than on a sample representative of the applicant population seems not to result in bias though it does result in difficulties in setting the cut off. Profit scoring is a promising line of research and the Basel 2 accord has had profound implications for the way in which credit applicants are assessed and bank policies adopted.     

On the parameterization of the CreditRisk model for estimating credit portfolio risk

The CreditRisk⁺ model is one of the industry standards for estimating the credit default risk for a portfolio of credit loans. The natural parameterization of this model requires the default probability to be apportioned using a number of (non-negative) factor loadings. However, in practice only default correlations are often available but not the factor loadings. In this paper we investigate how to deduce the factor loadings from a given set of default correlations. This is a novel approach and it requires the non-negative factorization of a positive semi-definite matrix which is by no means trivial. We also present a numerical optimization algorithm to achieve this.     

Structural models in consumer credit

We propose a structural credit risk model for consumer lending using option theory and the concept of the value of the consumer’s reputation. Using Brazilian empirical data and a credit bureau score as proxy for creditworthiness we compare a number of alternative models before suggesting one that leads to a simple analytical solution for the probability of default. We apply the proposed model to portfolios of consumer loans introducing a factor to account for the mean influence of systemic economic factors on individuals. This results in a hybrid structural-reduced-form model. And comparisons are made with the Basel II approach. Our conclusions partially support that approach for modelling the credit risk of portfolios of retail credit.     

Optimization strategies in credit portfolio management

This paper focuses on the application of an original global optimization algorithm, based on the hybridization between a genetic algorithm and a semi-deterministic algorithm, for the resolution of various constrained optimization problems for realistic credit portfolios. Results are analyzed from a financial point of view in order to confirm their relevance.     

Bayesian confidence intervals for probability of default and asset correlation of portfolio credit risk

We derive Bayesian confidence intervals for the probability of default (PD), asset correlation (Rho), and serial dependence (Theta) for low default portfolios (LDPs). The goal is to reduce the probability of underestimating credit risk in LDPs. We adopt a generalized method of moments with continuous updating to estimate prior distributions for PD and Rho from historical default data. The method is based on a Bayesian approach without expert opinions. A Markov chain Monte Carlo technique, namely, the Gibbs sampler, is also applied. The performance of the estimation results for LDPs validated by Monte Carlo simulations. Empirical studies on Standard & Poor’s historical default data are also conducted.     

The optimal resource portfolio under consumer choice and demand risk for vertically differentiated products

We study the optimal resource portfolio of a firm that sells two vertically differentiated products and utilizes resource flexibility and responsive pricing. We model this decision problem as a two-stage stochastic programming problem with recourse: In the first stage, the firm determines its resource mix and capacities so as to maximize the expected profit under demand uncertainty; in the second stage, uncertainty is resolved and the firm determines its production and pricing decision, constrained by its investment decision. We show that the objective function of this decision problem is not well-behaved (ie, it may have multiple local maxima). Using the concept of Pareto dominance, we reduce the feasible investment region, without loss of optimality, to one in which the objective function is well-behaved everywhere. This reduction allows us to derive the necessary and sufficient conditions for the optimal capacity decision and to gain insights.     

Adaptive integration for multi-factor portfolio credit loss models

We propose algorithms of adaptive integration for calculation of the tail probability in multi-factor credit portfolio loss models. We first modify the classical Genz-Malik rule, a deterministic multiple integration rule suitable for portfolio credit models with number of factors less than 8. Later on we arrive at the adaptive Monte Carlo integration, which essentially replaces the deterministic integration rule by antithetic random numbers. The latter can not only handle higher-dimensional models but is also able to provide reliable probabilistic error bounds. Both algorithms are asymptotic convergent and consistently outperform the plain Monte Carlo method.     

Modelling LGD for unsecured retail loans using Bayesian methods

Loss Given Default (LGD) is the loss borne by the bank when a customer defaults on a loan. LGD for unsecured retail loans is often found difficult to model. In the frequentist (non-Bayesian) two-step approach, two separate regression models are estimated independently, which can be considered potentially problematic when trying to combine them to make predictions about LGD. The result is a point estimate of LGD for each loan. Alternatively, LGD can be modelled using Bayesian methods. In the Bayesian framework, one can build a single, hierarchical model instead of two separate ones, which makes this a more coherent approach. In this paper, Bayesian methods as well as the frequentist approach are applied to the data on personal loans provided by a large UK bank. As expected, the posterior means of parameters that have been produced using Bayesian methods are very similar to the frequentist estimates. The most important advantage of the Bayesian model is that it generates an individual predictive distribution of LGD for each loan. Potential applications of such distributions include the downturn LGD and the stressed LGD under Basel II.     

Importance sampling for integrated market and credit portfolio models

A sophisticated approach for computing the total economic capital needed for various stochastically dependent risk types is the bottom-up approach. In this approach, usually, market and credit risks of financial instruments are modeled simultaneously. As integrating market risk factors into standard credit portfolio models increases the computational burden of calculating risk measures, it is analyzed to which extent importance sampling techniques previously developed either for pure market portfolio models or for pure credit portfolio models can be successfully applied to integrated market and credit portfolio models. Specific problems which arise in this context are discussed. The effectiveness of these techniques is tested by numerical experiments for linear and non-linear portfolios.     

Modelling LGD for unsecured personal loans: decision tree approach

The New Basel Accord, which was implemented in 2007, has made a significant difference to the use of modelling within financial organisations. In particular it has highlighted the importance of Loss Given Default (LGD) modelling. We propose a decision tree approach to modelling LGD for unsecured consumer loans where the uncertainty in some of the nodes is modelled using a mixture model, where the parameters are obtained using regression. A case study based on default data from the in-house collections department of a UK financial organisation is used to show how such regression can be undertaken.     

Modelling credit rating by fuzzy adaptive network

Human judgment plays an important role in the rating of enterprise financial conditions. The recently developed fuzzy adaptive network (FAN), which can handle systems whose behaviour is influenced by human judgment, appears to be ideally suited for the modelling of this credit rating problem. In this paper, FAN is used to model the credit rating of small financial enterprises. To illustrate the approach, the data of the credit rating problem is first represented by the use of fuzzy numbers. Then, the FAN network based on inference rules is constructed. And finally, the network is trained or learned by using the fuzzy number training data. The main advantages of the proposed network are the ability for linguistic representation, linguistic aggregation and the learning ability of the neural network.     

A profit-based scoring system in consumer credit: making acquisition decisions for credit cards

Consumer credit scoring is one of the most successful applications of quantitative analysis in business with nearly every major lender using charge-off models to make decisions. Yet banks do not extend credit to control charge-off, but to secure profit. So, while charge-off models work well in rank-ordering the loan default costs associated with lending and are ubiquitous throughout the industry, the equivalent models on the revenue side are not being used despite the need. This paper outlines a profit-based scoring system for credit cards to be used for acquisition decisions by addressing three issues. First, the paper explains why credit card profit models—as opposed to cost or charge-off models—have been difficult to build and implement. Second, a methodology for modelling revenue on credit cards at application is proposed. Finally, acquisition strategies are explored that use both a spend model and a charge-off model to balance tradeoffs between charge-off, revenue, and volume.     

A limit distribution of credit portfolio losses with low default probabilities

This paper employs a multivariate extreme value theory (EVT) approach to study the limit distribution of the loss of a general credit portfolio with low default probabilities. A latent variable model is employed to quantify the credit portfolio loss, where both heavy tails and tail dependence of the latent variables are realized via a multivariate regular variation (MRV) structure. An approximation formula to implement our main result numerically is obtained. Intensive simulation experiments are conducted, showing that this approximation formula is accurate for relatively small default probabilities, and that our approach is superior to a copula-based approach in reducing model risk.     

风险度量模型的研究

分析了方差法和半方差法作为风险测度的不足之处,考虑到资产离散程度和实际投资者的风险偏好,引入风险偏好系数,建立加权的半方差证券组合决策模型,作出了理论分析并给出了相应的数值比较结果。     

A study in the combination of two consumer credit scores

Credit scores measure the creditworthiness of individuals in a population of interest. In this paper, we employ the concepts of sufficiency and extraneousness to study the conditions under which scoring results can be improved through the combination of individual scores. The concept of sufficiency is used to identify scores that are dominant. Extraneousness is used to determine whether a particular score provides additional useful information relative to other scores. In addition, we employ a profit-based utility measure to evaluate the performance of different scores. We investigate the performance of a regression-based combination of a bureau credit score and an application credit score on a large historical data set. Our results show that the bureau score is dominated by the application score, but the bureau score is not extraneous to the combination. Thus, both scores contribute to the combined score, which indeed outperforms both of the scores upon which it is based.     

Liquidity and credit risk

The paper uses fuzzy measure theory to represent liquidity risk, i.e. the case in which the probability measure used to price contingent claims is not known precisely. This theory enables one to account for different values of long and short positions. Liquidity risk is introduced by representing the upper and lower bound of the price of the contingent claim computed as the upper and lower Choquet integral with respect to a subadditive function. The use of a specific class of fuzzy measures, known as g λ measures enables one to easily extend the available asset pricing models to the case of illiquid markets. As the technique is particularly useful in corporate claims evaluation, a fuzzified version of Merton's model of credit risk is presented. Sensitivity analysis shows that both the level and the range (the difference between upper and lower bounds) of credit spreads are positively related to the ‘quasi debt to firm value ratio’ and to the volatility of the firm value. This finding may be read as correlation between credit risk and liquidity risk, a result which is particularly useful in concrete risk-management applications. The model is calibrated on investment grade credit spreads, and it is shown that this approach is able to reconcile the observed credit spreads with risk premia consistent with observed default rate. Default probability ranges, rather than point estimates, seem to play a major role in the determination of credit spreads.     

A survey of the issues in consumer credit modelling research

Methods for assessing the credit risk when lending to consumers has been in operation for 50 years. Yet, there are probably now more opportunities and challenges for research into the development of this area than ever before. This paper surveys the development of the methodology, describes the current environment for consumer lending and seeks to identify some of the modelling areas and issues that are actively being researched or should be.     

Household risk aversion and portfolio choices

In practice, stock investment is one of the most important decisions made by households. The primary goal of this paper is to explain family investment decisions under the assumptions of household member’s preferences and efficient risk sharing based on the collective household model. In particular, by examining the absolute (relative) risk aversion of the household welfare function, we demonstrate how household’s portfolio allocation in stocks changes with family wealth. We examine two types of preference heterogeneity between family members: parameter heterogeneity and functional form heterogeneity. This study offers an alternative explanation of household portfolio choice corresponding with the observation that wealthier households tend to hold greater share of their wealth in risky assets. Specifically, if two decision-makers have standard constant relative risk aversion preference with different relative risk aversions in a household, family’s relative risk aversion decreases as household wealth increases (decreasing relative risk aversion).